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Experimental Data on Spin Structure Function
For 原子核特論講義資料
Yasuhiro SAKEMI (RCNP)E-mail : [email protected]
講義内容の追加資料等は、http://www.rcnp.osaka-u.ac.jp/~sakemi/lecture.htmlに随時掲載しますので、そちらも必要に応じて確認してください。
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核子スピンの起源
The spin structure of the proton :
Sz = = ΔΣ +ΔG +LZ
whereΔΣ≡Δu+Δd+Δs
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12
u u
dd
ss
du
u
• Quark spin contribution (ΔΣ ) to the nucleon spin is found to be small in inclusive DIS experiments (EMC,SMC,SLAC,HERMES)
– ΔΣ≡Σ q(Δq + Δq ) ~ 0.2 ... 0.4
• What are the contributions of the different quark flavors ? – The answer is only partially known. – e.g. Strange sea polarization Δs has not yet been measured.
• Further Study !– Hadron coincidence measurement in the polarized DIS– Particle identification with Ring Imaging Cherenkov Counter
(RICH) – Flavor tagging with the final state produced hadrons
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Quark Polarization (Inclusive)
Proton Spin Structure Function g1p(x)
≃≃≃
– g1h(x,Q2) Σf ef
2Δqf(x,Q2)– F1
h(x,Q2) Σf ef2 qf(x,Q2)
A1≃ =
x
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Quark Polarization (Inclusive)
Neutron Spin Structure Function g1n(x)
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Quark Polarization (Semi-Inclusive)
Hadron Asymmetries
• Statistics of proton data ~ high • Data given at mean Q2 of each x• Error :
– Error bars of HERMES : statistical uncertainties– Bands are HERMES systematic error– Error bars of SLAC and SMC : total uncertainties
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Quark Polarization (Semi-Inclusive)
Flavor decomposition of PDF
• Flavor decomposition of quark polarizations as a function of x at measured Q2
• Sea assumption (flavor independent polarization) : – Δqs Δus Δds Δs Δu Δd Δs– qs us ds s u d s
• Result insensitive to sea assumption – another assumption : flavor symmetric sea : checked
≡ = = = = =
Flavor Decomposition of the Polarized Quark Distributions in the Nucleon fromInclusive and Semi-Inclusive Deep-inelastic ScatteringK. Ackerstaff et al, Phys. Lett. B464 (1999) 123-134
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Quark Polarization (Semi-Inclusive)
Polarized Quark Distributions
• Polarized valence and sea quark distributions atQ2 = 2.5 GeV2
• Dotted line : Gehrmann and Stirling (Gluon A, LO)• Sea assumptions :
– HERMES : flavor independent polarization– SLAC : flavor symmetric
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Quark Polarization (Semi-Inclusive)
Comparison to Parametrizations
• Polarized quark distributions at Q2 = 2.5 GeV2 compared to parametrizations
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Quark Polarization (Sum Rule)
xΔqNS and Bjorken Sum Rule
• Non-singlet contribution ΔqNS = (Δu+Δu-Δd-Δd) is directly related to the spin structure functions according to ΔqNS = 6(g1
p(x)-g1n(x)) .
• ΔqNS at Q2=2.5 GeV2 compared to paramerizations extracted from inclusive data
• Bjorken Sum Rule : model independent – ∫0
1ΔqNS (x) dx = |ga/gv|×CQCD
– (experiment) 0.84±0.07±0.06– (prediction:Bjorken) 1.01±0.05– consistent
• Nucleon
integral
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Quark Polarization (Sum Rule)
xΔq8
• Octet combination xΔq8=x(Δu+Δu+Δd+Δd-2(Δs+Δs))at Q2=2.5GeV2 assuming a flavor symmetric sea (open circle) or a flavor independent sea (full circle)
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Quark Polarization (Moment)
Integrals over measured range
• Integral over measured range is obtained as
– Δq = Σi ( |i∫xixi+1 q(x) dx )
– where (Δq/q)|i is constant within each bin [xi, xi+1]
» HERMES SMC– Δuv 0.52±0.05 ±0.08 0.59±0.08 ±0.07– Δdv -0.18 ±0.10 ±0.13 -0.33±0.11 ±0.09– Δu -0.01 ±0.02 ±0.03 0.02±0.03 ±0.02– Δd -0.02 ±0.03 ±0.04 0.02±0.03 ±0.02– Δs -0.01 ±0.02 ±0.02 0.01±0.03 ±0.02
• Comparison of HERMES and SMC integrals in the HERMES x-range of 0.023 ≤ x ≤ 0.6 . All values given at Q2=2.5 GeV2
• Agreement of HERMES and SMC results
Δqq
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Quark Polarization (Moment)
Moments
• Flavor decomposition (Q2=2.5 GeV2)– comparison with SU(3) prediction
(J.Ellis and M.Karliner, Phys.Lett.B341(1995)397) » total integral prediction
– Δu+Δu 0.57±0.02±0.03 0.66±0.03– Δd+Δd -0.25±0.06±0.05 -0.35±0.03– Δs+Δs -0.01±0.03±0.04 -0.08±0.02
• Comparison with Lattice calculation (Q2=2.5 GeV2)– M.Gockeler, Phys.Lett. B414 (1997) 81
» total integral prediction– Δuv 0.57±0.05±0.08 0.84±0.05 (Q2=5)– Δdv -0.22±0.11±0.13 -0.25±0.02 (Q2=5)
• Singlet (Δq0), Triplet(Δq3), and Octet(Δq8) (Q2=2.5 GeV2)» total integral prediction
– Δq0 0.30±0.04±0.09 0.23±0.04 (SU(3))– Δq3 0.84±0.07±0.06 1.01±0.05 (Bjorken)– Δq8 0.32±0.09±0.10 0.35±0.07 (non-SU(3))– Δq8
* 0.33±0.10±0.11 0.46±0.03 ((3F-D)×CQCD)– where Δq8 : use flavor asymmetric polarized sea
Δq8*:use flavor symmetric polarized sea
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Gluon Polarization
Measured Asymmetry A//(pTh+,pT
h-)
• systematic error ~ 8 % • checks that have been performed on the data
– e+ - h+ misidentification– particle identification cut variation– momentum (~z) cut variation– consistent result obtained using identified pions only
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Gluon Polarization
Region of interest
• Systematic error ~ 8 %
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Gluon Polarization
MC data comparison
• Comparisons of measured cross sections with predictions of model implemented in PYTHIA
– solid black: total– solid red: PGF– dashed blue: QCDC– dotted black: soft VMD
• data are compared in a region where PYTHIA model is independent of pT
min cut-off parameter• Other comparisons:
– other distributions: e.g. Δφ…– other regions of phase space: e.g. in regions
dominated by soft VMD
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Gluon Polarization
Fraction of subprocesses
• The unpolarized model of the data is used to extract the unpolarized fi’s :
• The negative asymmetry is observed where PGF is expected to dominate.
• Significant uncertainty from contribution due to hadronic structure of the photon.
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Gluon Polarization
Gluon polarization
• ΔG/G = 0.41 ±0.18 (stat.) ±0.03 (exp.syst.)at <xG> = 0.17 and <pT
2> = 2.1 GeV2
• Large uncertainty from contribution and unknown spin asymmetry of hadronic photon. If only a dilution, value of ΔG/G will increase but significance will not change.
ΔG/G=-1
ΔG/G=0.41
ΔG/G=0
ΔG/G= +1
Measurement of the Spin Asymmetry in the Photoproduction of Pairs of High-pTHadrons at HERMESA. Airapetian et al, Phys. Rev. Lett. 84 (2000) 2584-2588
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Flavor Asymmetry
フレーバー非対称性:d-u 分布
• 核子中のseaクォーク分布の非対称性– (d-u)/(u-d) > 0 : 反ダウンクォーク分布が excess
• meson cloud model による実験データの解釈– p -> n + π+ : d の分布が多くなっている。
• ストレンジクォークの分布は?
– s(x) と s(x) の分布が非対称の可能性がある。– Meson cloud model : p -> Λ + K – RICHを用いてストレンジクォーク分布の測定
= +p nπの雲
(uud) (udd) (ud)
The Flavor Asymmetry of the Light Quark Sea from Semi-inclusive Deep-inelasticScatteringK. Ackerstaff et al, Phys. Rev. Lett.25, vol. 81 (1998) 5519-5523
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Experiment (Polarized Electron Beam)
The polarized electron beam at HERA
• Self-polarization by emission of synchrotron radiation– pb(t) = Pb
max[1-exp(-t/τ)]• Spin rotators longitudinal polarization at HERMES IP• 2 Compton polarimeters• Average beam polarization <pb> ~ 55 %
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Experiment (Spectrometer)
The HERMES experiment
• 27.5 GeV longitudinally polarized e-beam– polarization: Pbeam ~ 55 %
• Internal Target– longitudinally polarized atoms: H, D, 3He
• Kinematic range– 0.02 < x < 0.8 for Q2 > 1 GeV2 and W > 2 GeV
• Track reconstruction: 57 tracking chamber planes– δP/P = 0.7 % ~1.3 % , δθ < 0.6 mrad
• Particle Identification– 4 PID detectors : electron-hadron separation
The HERMES SpectrometerK. Ackerstaff et al., NIM A417 (1998) 230-265
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Experiment (Polarized Target)
Polarized target
• 40 cm long open-ended storage cell • Undiluted internal targets :
– H,D,3He longitudinally polarized atoms• Laser driven polarized 3He (1995) :
– PT=46 %, =1015 N/cm2, Δtflip ~ 10 min• Atmic beam source for polarized H/D (1996 ~ 1999) :
– PT=92 %, =7 ×1013 N/cm2, Δtflip ~ 1 min• Unpolarized gases :
– H,D,3He,14N,83Kr…, 1015 ~ 1017 N/cm2
Beam-Induced Nuclear Depolarisation in a Gaseous Polarised Hydrogen TargetK. Ackerstaff et al., Phys. Rev. Lett. 82 (1999) 1164-1168
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Experiment Event reconstruction at HERMES
トラック再構成
Vertexchamber
内部標的
Frontchamber
MagnetMagnetchamber
Backchamber
Cherenkov
Hodoscope
TRDCalorimeter
e+
π+
π‐
PID: step1:positron / hadron separation• Calorimeter, Preshower, TRD, Cerenkov• 99 % positron identification efficiency with 1 % hadron contamination
PID: step2:Hadron ID :RICH(π,K,p)• Method1: Inverse Ray Tracing (IRT):Reconstruction of the cherenkov angle by IRT using PMT hits and tracking info.
• Method2: Direct Ray Tracing (DRT):Construction of the expected hitprobability densities for a giving track and given particle type hypotheses by DRT
Detail : reported at JPS meeting on 25-Sep,1999
粒子識別
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Experiment (Particle Identification : PID)
Ring Imaging Cherenkov 検出器(RICH)
• 1998年6月に完成
エアロジェル発光体:エアロジェルタイル
17×5×5=425枚ひとつのタイルのサイズは 11 cm×11 cm×1 cm
200 cm
60 cm
5 cm
120 cm
150 cm
300 cm
Photon Detector反射鏡
外観図
側面図
Photons
Aerogel Tiles
Mirror
C4F10
PMTs plane
Aluminium
エアロジェル発光体の内部構造
Charged particle
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• RICH:チェレンコフ放射角度から速度測定(v):
• 磁気スペクトロメータ:運動量測定(p):
粒子の質量 (m) 決定:粒子識別
Experiment (PID)
RICHによる粒子識別
チェレンコフ放射角度と運動量の関係
Aerogeln=1.03
C4F10n=1.0014
e
π K
p
e
πK
p0
0.05
0.1
0.15
0.2
0.25
0 4 8 12 16 20
π
Kp
(1) エアロジェルとC4F10に
よるチェレンコフ放射角度の情報を用いる(2) threshold type cherenkov counter としての情報を用いる
この2つの方法を組み合わせて粒子識別
P (GeV/c)
粒子識別方法
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Experiment (PID) RICHの特徴
• シリカ・エアロジェルとC4F10ガスを用いた2重発光体RICH
• シリカ・エアロジェルを世界で初めてRICHの発光体として実
際の実験に用いた
• 2 GeV/c から20 GeV/c の広い運動量領域にわたってπ,K,pのハドロンを識別
ハドロン運動量分布
Even
ts
1
10
10
10
2
3
0 10 20Momentum(GeV/c)
Target: proton
K, p
p
π
π, K
3.8 GeV/c 13.6 GeV/c
(threshold type cherenkov)
RICH PID
Beam Energy27.5 GeV/c
(1)HERMESで発生するハドロンのほぼ全運動量領域をcover(2)測定されるハドロンのYield:増加:πのYield~RICH以前の閾値型チェレンコフ検出器に比べて約2倍増加
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Experiment (PID)
エアロジェル発光体の外観
• タイル 5×17列×5層からなる発光体
Optical characterization of n=1.03 silica aerogel used as radiator in the RICH of HERMESNIM A440 (2000) 338
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Experiment (PID)Photon Detector
Photon detector• Hexagonal grid of 1934 PMTs per detector half • PMT Type: Philips XP1911/UV • 3/4 inch PMT diameter• Active area increased to 91 % by reflective funnel cones
Photo cathode
funnel
23.3 mm
Front view Side view
Readout• 3864 PMT channels (top and bottom together)• No analog information: use LeCroy PCOS4 system• 1024 PMTs -> 64 preamp cards -> 4 back planes with
FPGA -> 1 VME module
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Experiment (PID)
RICHの全体写真
• エアロジェル発光体をインストールする直前
• 反射鏡に光電子倍増管が映っているのが見える
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Experiment (PID)
RICHにより得られる情報
• Photon Detector がヒットした位置• 2種類の発光体(エアロジェルとC4F10)により2種類のチェレンコフリングが生じる
• リングの半径の違いが粒子の速度-種類を反映
典型的なイベント(e+P -> e’ + π X)の RICH によるリングイメージ
Top Detector
Bottom Detector
Side View
3.1 GeV/c π 中間子
4.5 GeV/c 電子
-
‐
RICH
C4F10ガスからのチェレンコフ光子によるリング
エアロジェルからのチェレンコフ光子によるリング
1934本の光電子倍増管で構成された検出面
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• RICH:チェレンコフ放射角度から速度測定(v):
• 磁気スペクトロメータ:運動量測定(p):
粒子の質量 (m) 決定:粒子識別
Experiment (PID)
RICHによる粒子識別
質量2乗分布によるπ、K分離
00 0.4Mass (GeV )2 2
2<P<3 GeV/c
π
K
6000
Yie
ldEventselection
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Experiment (PID)
RICHの解析結果
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Experiment (Δq) Δq extraction
電子
仮想光子
核子
Targetfragment
Currentfragment
ee’
Nh
X’
X
ΔS(x) , Δu(x)-Δd(x) , Δq(x)
ef2・qf(x)・Df
h(z) Δqf(x)Σf’ ef’
2・qf’(x)・Df’h(z) qf(x)A1
h (x,z) = Σf A=P・Q
Purity FragmentationFunction
Parton densityfunction
Δq/q = P-1 ・A
Statistical error :Systematic error:(1) Ambiguity of experiment : RICH PID etc… many things(2) Δq extraction method : purity method / analytic method(3) unpol parton distribution function : GRV/CTEQ/…(4) Fragmentation Function :
- Experimental Data : EMC/HERMES/…- Theoretical Model :
F.F/Lund/Cluster/Spectator/UCLA …(5) others…
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Experiment (Δq)
Monte Carlo Projection
Projection based on 8 × 106 DIS events with semi-inclusive K± asymmetries.
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Nuclear Transparency
実験結果
• lc > R14N において Hadronic ISI により T14N は減少
• 様々な原子核標的を用いて lc依存性を測定する必要がある
• Glauber 近似によるモデルの予想– γ*N →ρ0N の散乱振幅がρ0Nの弾性散乱に比例するとする
– lc≫ RA における effective ISI が自然に導入できる• 原子核
=λ
γ* ρ ρ’ρ
N N N’N’
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